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Mathematical modeling and simulation of mechano-chemical effect on two-phase avascular tumor

Author

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  • Sweta Sinha

    (School of Mathematics, Thapar Institute of Engineering and Technology, Patiala 1470 04, India)

  • Paramjeet Singh

    (School of Mathematics, Thapar Institute of Engineering and Technology, Patiala 1470 04, India)

Abstract

In this paper, we derive the mathematical model that allows chemotaxis in avascular tumor growth in a two-phase medium. The two phases are the viscous cell phase and the inviscid fluid phase. The conservation of mass–momentum is incorporated in each phase, and appropriate constitutive laws are applied to formulate the governing equations. Further, these equations are simplified into three main variables: cell volume fraction, cell velocity, and nutrient concentration. These variables generate a coupled system of nonlinear partial differential equations. A numerical scheme based on the finite volume method is applied to approximate the solution of cell volume fraction. The finite element method is applied to approximate the solutions of cell velocity and nutrient concentration. In this research paper, we investigate tumor growth when tumor cells move along a fluid containing a diffusible nutrient to which the cells are drawn. We perform some numerical simulations to show the effect of the parameters. The findings of this literature are compatible with the existing literature.

Suggested Citation

  • Sweta Sinha & Paramjeet Singh, 2022. "Mathematical modeling and simulation of mechano-chemical effect on two-phase avascular tumor," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 33(05), pages 1-22, May.
    • Handle: RePEc:wsi:ijmpcx:v:33:y:2022:i:05:n:s0129183122500632
    DOI: 10.1142/S0129183122500632
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    Cited by:

    1. Miranda, Luiza M.S. & Souza, Andre M.C., 2023. "Fractality in tumor growth at the avascular stage from a generalization of the logistic-Gompertz dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 618(C).

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